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As Relaxed said, taking the train is probably a good idea.
If you don't mind which order you visit the cities in, there is a sleeper train from Franfurt to Prague, it leaves at 00.54 so you could leave on the day that you finish work and arrive in Prague the morning after, advance tickets seem to be available at €49 in a seat or €60 in a bunk bed.
From ...

It's very rushed as there are many things to see in these cities and transportation will cost you dearly relative to the time spent in each place but obviously I can also see why you would want to do that and I think it should be doable.
Because you have so little time, the obvious choice between Frankfurt and Paris or Paris and Amsterdam will be the train. ...

It takes about 50 minutes to get there and you have to change from subway to bus and then walk for a quarter of an hour. This wil cost you EUR 4.81 one way.
Muiden is too small a place to spend more than a couple of hours, so you'll probably want to return to Amsterdam.
Hiring a bicycle will cost you about 8 EURO. See ...

In the case of Amsterdam, what you're looking for are (ex-)squats. Ex-, because squatting in Amsterdam became illegal in late 2010. "What's up with Amsterdam" has some back-story for that.
One of the most famous ones is Squat Vrankrijk, which is right in the center, on Spuistraat.
You can find these kind of places in the Canal Belt, Old Center, but ...

On megabus.co.uk, you can find an Amsterdam - London ticket for 17.50 pounds. Then, a London to Dublin ticket can set you back as little as 15 pounds.
Both connections include a ferry.
Occasionally, Megabus offers deals of 10 pounds for each of the above legs. But, note that trying to book the whole journey as one trip is almost always (if not always) more ...

Your cheapest option is probably a flight, but this is not certain. Easyjet appears to have cheap flights between Amsterdam and Belfast, although I'm not sure how many hidden fees are added to their advertised price. If not flying, between Amsterdam and London, a cheap option is the Dutch Flyer, which will set you back £49: Dutch Flyer connects you from ...

The cheapest way to travel from Amsterdam to Paris is by hitch-hiking.
Failing that, early-booked buses are cheapest. For example, if I search now for a Eurolines bus on a weekday late May, I find tickets as cheap as 9€. You want to search for Promo tickets, indicated in dark red in the fare calendar.
Screen-capture of Eurolines booking system
There ...